Problem: Simplify the following expression: $\dfrac{24p^3}{15p^2}$ You can assume $p \neq 0$.
$ \dfrac{24p^3}{15p^2} = \dfrac{24}{15} \cdot \dfrac{p^3}{p^2} $ To simplify $\frac{24}{15}$ , find the greatest common factor (GCD) of $24$ and $15$ $24 = 2 \cdot 2 \cdot 2 \cdot 3$ $15 = 3 \cdot 5$ $ \mbox{GCD}(24, 15) = 3 $ $ \dfrac{24}{15} \cdot \dfrac{p^3}{p^2} = \dfrac{3 \cdot 8}{3 \cdot 5} \cdot \dfrac{p^3}{p^2} $ $\phantom{ \dfrac{24}{15} \cdot \dfrac{3}{2}} = \dfrac{8}{5} \cdot \dfrac{p^3}{p^2} $ $ \dfrac{p^3}{p^2} = \dfrac{p \cdot p \cdot p}{p \cdot p} = p $ $ \dfrac{8}{5} \cdot p = \dfrac{8p}{5} $